Melt the oil and butter in a medium saucepan over medium heat. Add the shallot and garlic season with the salt and pepper, and cook until tender, about 4 minutes. Stir in the peaches, brown sugar, cherries, and mustard. Cook, stirring occasionally, until peaches get nice and juicy and turn into a thick chunky compote, about 8 minutes. Cool and serve at room temperature with chicken or pork.